Bring a pot of salted water to a boil. Add the lemon halves and garlic. Submerge a large heatproof strainer in the water. Soak the onion in ice water while the seafood cooks. Fill a large bowl with ice water and set aside.

Add the shrimp, scallops, and calamari to the strainer and cook for 2 minutes (until shrimp is pink), remove and plunge in ice water. Return the strainer to the boiling water and add the mussels; cook until the shells open. Drain the seafood from the water and remove the mussels from the shells. Pat dry.

Drain the red onion and pat dry. Combine seafood, onion, celery, fennel ,olives and parsley the in a large bowl. Drizzle with lemon juice and oil and season with salt and pepper. Let it sit at least 30 minutes or refrigerate up to 4 hours.